"Contest" vs. "competition"

Solution 1:

I think the words are more synonomous and interchangable than you've described in your question. Here are some of my reservations:

• Contest isn't always associated with brute strength (the term beauty contest comes to mind)
• Either a contest or a competition could have a prize (in Olympics gymnastics, for example, there is the all-around competition).
• Competition seems no less applicable to a one-time event than the word contest (observe how this reporter talks about the outdoor cooking competition).

With all that said, however, I still agree with your final choice: I'd probably vote for programming contest over programming competition; that wording seems to emphasize that the event is intended to be more fun, and less cutthroat.

One other word you might consider is challenge: The 2012 Programming Challenge.

Solution 2:

Contest refers to conflicts more generally. It's first meaning is the legal one, where different parties contest something in court (it comes from the Latin for calling a witness), and can refer to military conflict, elections etc.

Compete refers to a case where people try to do better than each other at something (business would be another example where we talk of competition and competitors).

While this may mean the former seems the more aggressive, it's also more applicable to cases where what one is contesting isn't ones competitors, but other conditions. A case where everyone who attained a particular result was considered to have won would be a contest (they're struggling against whatever the challenge is, and may or may not achieve the goal) but not a competition (another participant doing well does not make their winning any harder, so they aren't competing).

For this reason, while they're close synonyms in many cases, contest has a stronger nuance of reflecting the challenge itself, and competition of doing better than other participants.

Solution 3:

Contest suggests playing a game for the game's sake just to see who would win, or maybe playing for candy. But competition suggests playing the game in order to get some big reward, where the reward and the achievement is the only thing that is important, and there may be no pleasure in the game.